Maximal compatible splitting and diagonals of Kempf varieties

Niels Lauritzen[1]; Jesper Funch Thomsen[1]

  • [1] Aarhus University Department of Mathematical Sciences Bygning 1530 Ny Munkegade 118 8000 Århus C (Denmark)

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 6, page 2543-2575
  • ISSN: 0373-0956

Abstract

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Lakshmibai, Mehta and Parameswaran (LMP) introduced the notion of maximal multiplicity vanishing in Frobenius splitting. In this paper we define the algebraic analogue of this concept and construct a Frobenius splitting vanishing with maximal multiplicity on the diagonal of the full flag variety. Our splitting induces a diagonal Frobenius splitting of maximal multiplicity for a special class of smooth Schubert varieties first considered by Kempf. Consequences are Frobenius splitting of tangent bundles, of blow-ups along the diagonal in flag varieties along with the LMP and Wahl conjectures in positive characteristic for the special linear group.

How to cite

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Lauritzen, Niels, and Thomsen, Jesper Funch. "Maximal compatible splitting and diagonals of Kempf varieties." Annales de l’institut Fourier 61.6 (2011): 2543-2575. <http://eudml.org/doc/219739>.

@article{Lauritzen2011,
abstract = {Lakshmibai, Mehta and Parameswaran (LMP) introduced the notion of maximal multiplicity vanishing in Frobenius splitting. In this paper we define the algebraic analogue of this concept and construct a Frobenius splitting vanishing with maximal multiplicity on the diagonal of the full flag variety. Our splitting induces a diagonal Frobenius splitting of maximal multiplicity for a special class of smooth Schubert varieties first considered by Kempf. Consequences are Frobenius splitting of tangent bundles, of blow-ups along the diagonal in flag varieties along with the LMP and Wahl conjectures in positive characteristic for the special linear group.},
affiliation = {Aarhus University Department of Mathematical Sciences Bygning 1530 Ny Munkegade 118 8000 Århus C (Denmark); Aarhus University Department of Mathematical Sciences Bygning 1530 Ny Munkegade 118 8000 Århus C (Denmark)},
author = {Lauritzen, Niels, Thomsen, Jesper Funch},
journal = {Annales de l’institut Fourier},
keywords = {Special linear group; Schubert variety; Frobenius splitting; maximal multiplicity; Wahl’s conjecture; Wahl's conjecture},
language = {eng},
number = {6},
pages = {2543-2575},
publisher = {Association des Annales de l’institut Fourier},
title = {Maximal compatible splitting and diagonals of Kempf varieties},
url = {http://eudml.org/doc/219739},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Lauritzen, Niels
AU - Thomsen, Jesper Funch
TI - Maximal compatible splitting and diagonals of Kempf varieties
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 6
SP - 2543
EP - 2575
AB - Lakshmibai, Mehta and Parameswaran (LMP) introduced the notion of maximal multiplicity vanishing in Frobenius splitting. In this paper we define the algebraic analogue of this concept and construct a Frobenius splitting vanishing with maximal multiplicity on the diagonal of the full flag variety. Our splitting induces a diagonal Frobenius splitting of maximal multiplicity for a special class of smooth Schubert varieties first considered by Kempf. Consequences are Frobenius splitting of tangent bundles, of blow-ups along the diagonal in flag varieties along with the LMP and Wahl conjectures in positive characteristic for the special linear group.
LA - eng
KW - Special linear group; Schubert variety; Frobenius splitting; maximal multiplicity; Wahl’s conjecture; Wahl's conjecture
UR - http://eudml.org/doc/219739
ER -

References

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  10. V. Lakshmibai, Kempf varieties, J. Indian Math. Soc. (N.S.) 40 (1976), 299-349 (1977) Zbl0447.14014MR506317
  11. V. Lakshmibai, V. B. Mehta, A. J. Parameswaran, Frobenius splittings and blow-ups, J. Algebra 208 (1998), 101-128 Zbl0955.14006MR1643983
  12. Venkatramani Lakshmibai, Komaranapuram N. Raghavan, Parameswaran Sankaran, Wahl’s conjecture holds in odd characteristics for symplectic and orthogonal Grassmannians, Cent. Eur. J. Math. 7 (2009), 214-223 Zbl1200.14100MR2506962
  13. V. B. Mehta, A. J. Parameswaran, On Wahl’s conjecture for the Grassmannians in positive characteristic, Internat. J. Math. 8 (1997), 495-498 Zbl0914.14021MR1460897
  14. V. B. Mehta, A. Ramanathan, Frobenius splitting and cohomology vanishing for Schubert varieties, Ann. of Math. (2) 122 (1985), 27-40 Zbl0601.14043MR799251
  15. David Mumford, The red book of varieties and schemes, 1358 (1999), Springer-Verlag, Berlin Zbl0658.14001MR1748380
  16. Jonathan Wahl, Gaussian maps and tensor products of irreducible representations, Manuscripta Math. 73 (1991), 229-259 Zbl0764.20022MR1132139
  17. Oscar Zariski, Pierre Samuel, Commutative algebra. Vol. II, (1975), Springer-Verlag, New York Zbl0313.13001MR389876

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